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Journal articles on the topic 'Hartree-Fock approximation'

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Published: 4 June 2021

Last updated: 29 July 2024

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1

LI, BAO-CHUN, and LI-LI WANG. "ENTROPY IN SCALAR O(N) MODEL WITH A SPONTANEOUSLY BROKEN SYMMETRY." International Journal of Modern Physics A 24, no. 30 (December 10, 2009): 5725–36. http://dx.doi.org/10.1142/s0217751x09047363.

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We investigate the entropy in a scalar O(N) model with a spontaneously broken symmetry. The Cornwall–Jackiw–Tomboulis formalism is applied to derive the entropy in the Hartree and Hartree–Fock approximations. In contrast to the Hartree approximation where the particles are quasiparticles with vanishing decay width, the Hartree–Fock approximation contains exchange contributions, which lead to nonzero decay width. We find that the sunset diagrams contribution is very small. Furthermore, the decay widths from these diagrams are discussed in the weak and strong coupling cases.

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2

Huber, H., F. Weber, M. K. Weigel, and Ch Schaab. "Neutron Star Properties with Relativistic Equations of State." International Journal of Modern Physics E 07, no. 03 (June 1998): 301–39. http://dx.doi.org/10.1142/s0218301398000130.

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We study the properties of neutron stars adopting relativistic equations of state of neutron star matter, calculated in the framework of the relativistic Brueckner–Hartree–Fock approximation for electrically charge neutral neutron star matter in beta–equilibrium. For higher densities more baryons (hyperons etc.) are included by means of the relativistic Hartree– or Hartree–Fock approximation. The special features of the different approximations and compositions are discussed in detail. Besides standard neutron star properties special emphasis is put on the limiting periods of neutron stars, for which the Kepler criterion and gravitation–reaction instabilities are considered. Furthermore the cooling behaviour of neutron stars is investigated, too. For comparison we also give the outcome for some nonrelativistic equations of state.

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3

Gómez, J. M. G., and C. Prieto. "The Hartree-Fock seniority approximation." Nuclear Physics A 452, no. 3 (April 1986): 462–76. http://dx.doi.org/10.1016/0375-9474(86)90209-5.

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4

Huber, H., M. K. Weigel, and F. Weber. "Compatibility of Neutron Star Masses and Hyperon Coupling Constants." Zeitschrift für Naturforschung A 54, no. 1 (January 1, 1999): 77–82. http://dx.doi.org/10.1515/zna-1999-0110.

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Abstract It is shown that the modern equations of state for neutron star matter based on microscopic calculations of symmetric and asymmetric nuclear matter are compatible with the lower bound on the maximum neutron-star mass for a certain range of hyperon coupling constants, which are constrained by the binding energies of hyperons in symmetric nuclear matter. The hyperons are included by means of the relativistic Hartree-or Hartree-Fock approximation. The obtained couplings are also in satisfactory agreement with hypernuclei data in the relativistic Hartree scheme. Within the relativistic Hartree-Fock approximation, hypernuclei have not been investigated so far.

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5

SITKO, PIOTR. "STATISTICS TRANSMUTATIONS IN TWO-DIMENSIONAL SYSTEMS AND THE FRACTIONAL QUANTUM HALL EFFECT." Modern Physics Letters B 08, no. 06 (March 10, 1994): 375–80. http://dx.doi.org/10.1142/s021798499400039x.

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Statistics transmutations to superfermions in fractional quantum Hall effect systems are considered in the Hartree-Fock approximation and in the RPA. The Hartree-Fock ground state energy shows that the transmutations are not energetically preferable. Within the RPA it is found that the system exhibits a fractional quantum Hall effect.

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6

Zhang, Yi-Cheng. "Directed polymers in Hartree-Fock approximation." Journal of Statistical Physics 57, no. 5-6 (December 1989): 1123–28. http://dx.doi.org/10.1007/bf01020051.

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7

PEREZ MARTINEZ, A., and A. CABO. "HARTREE-FOCK APPROXIMATION FOR COULOMB INTERACTING ANYON GAS IN A MAGNETIC FIELD." Modern Physics Letters B 05, no. 24n25 (October 1991): 1703–12. http://dx.doi.org/10.1142/s0217984991002057.

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Dyson equations for a Coulomb interacting anyon gas in a magnetic field are obtained and solved in the Hartree-Fock approximation. The states recently proposed by Greiter and Wilczek naturally arise from the Hartree-Fock solution. The electron self energies are calculated in the case when only the lowest Landau level is occupied.

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8

SITKO, PIOTR, and LUCJAN JACAK. "HARTREE–FOCK GROUND STATE OF THE COMPOSITE FERMION METAL." Modern Physics Letters B 09, no. 14 (June 20, 1995): 889–94. http://dx.doi.org/10.1142/s0217984995000851.

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Within the Hartree–Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the single-particle exchange at the Fermi momentum. It is shown that the Hartree–Fock result brings no corrections to the RPA Fermi velocity.

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9

BARAN, A., A. STASZCZAK, J. DOBACZEWSKI, and W. NAZAREWICZ. "COLLECTIVE INERTIA AND FISSION BARRIERS WITHIN THE SKYRME-HARTREE-FOCK THEORY." International Journal of Modern Physics E 16, no. 02 (February 2007): 443–51. http://dx.doi.org/10.1142/s0218301307005879.

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Spontaneous fission barriers, quadrupole inertia tensor, and zero-point quadrupole correlation energy are calculated for 252,256,258 Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing collective inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.

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10

Arora, Gunjan, and B. L. Ahuja. "Compton Scattering and Electronic Properties of Tungsten Ditelluride." Solid State Phenomena 209 (November 2013): 107–10. http://dx.doi.org/10.4028/www.scientific.net/ssp.209.107.

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We report the first ever isotropic experimental Compton profile of tungsten ditelluride using 20 Ci 137Cs Compton spectrometer. To compare our experimental data, we have also computed the Compton profiles, energy bands, density of states and band gap using Hartree-Fock and density functional theory within linear combination of atomic orbitals. The measured data is found to be in better accordance with the generalised gradient approximation of density functional theory than Hartree-Fock and local density approximation. We have discussed the nature of bonding in WTe2 using energy bands and density of states.

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11

BACH, VOLKER, ELLIOTT H. LIEB, and MARCOS V. TRAVAGLIA. "FERROMAGNETISM OF THE HUBBARD MODEL AT STRONG COUPLING IN THE HARTREE–FOCK APPROXIMATION." Reviews in Mathematical Physics 18, no. 05 (June 2006): 519–43. http://dx.doi.org/10.1142/s0129055x06002735.

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As a contribution to the study of the Hartree–Fock theory, we prove rigorously that the Hartree–Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential μ) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree–Fock theory, we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.

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12

Hong, Suklyun, and G. D. Mahan. "Temperature dependence of the Hartree-Fock approximation." Physical Review B 50, no. 11 (September 15, 1994): 7284–90. http://dx.doi.org/10.1103/physrevb.50.7284.

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13

BOGOLUBOV, N. N., and A. V. SOLDATOV. "HARTREE–FOCK–BOGOLUBOV APPROXIMATION IN THE MODELS WITH GENERAL FOUR-FERMION INTERACTION." International Journal of Modern Physics B 10, no. 05 (February 28, 1996): 579–97. http://dx.doi.org/10.1142/s0217979296000246.

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An approach is proposed which allows one to investigate dynamical and thermodynamical properties of models with four-fermion interaction of general type. The approach combines ideas of the standard Bogolubov's approximating Hamiltonian method for the models with separable interaction with the method of Hartree–Fock approximation based on the ideas of self-consistency.

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14

SHIMODA, YUICHI, TATSUYA NAKAJIMA, and ANJU SAWADA. "HARTREE–FOCK–BOGOLIUBOV STUDIES OF BILAYER ν = 2 QUANTUM HALL SYSTEMS." Modern Physics Letters B 19, no. 11 (May 10, 2005): 539–48. http://dx.doi.org/10.1142/s0217984905008517.

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Excitation spectra in bilayer quantum Hall systems at total Landau-level filling ν = 2 are studied by the Hartree–Fock–Bogoliubov (HFB) approximation. The systems have the spin degrees of freedom in addition to the layer degrees of freedom described in terms of pseudospin. On the excitation spectrum from the spin-singlet and pseudospin-polarized ground state, this approximation fully preserves the spin rotational symmetry and thus can give both spin-triplet and spin-singlet excitations systematically. It is also found that the ground state is pseudospin squeezed because of pseudospin correlations and that the HFB approximation can describe ground-state properties better than other approximations.

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15

Cui, Qiang, and Marcus Elstner. "Density functional tight binding: values of semi-empirical methods in an ab initio era." Phys. Chem. Chem. Phys. 16, no. 28 (2014): 14368–77. http://dx.doi.org/10.1039/c4cp00908h.

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16

JOHNSON, CALVIN W., and IONEL STETCU. "SHORTCUTS TO NUCLEAR STRUCTURE: LESSONS IN HARTREE–FOCK, RPA, AND THE NO-CORE SHELL MODEL." International Journal of Modern Physics E 14, no. 01 (February 2005): 57–65. http://dx.doi.org/10.1142/s0218301305002771.

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While the no-core shell model is a state-of-the-art microscopic approach to low-energy nuclear structure, its intense computational requirements lead us to consider time-honored approximations such as the Hartree–Fock (HF) approximation and the random phase approximation (RPA). We review RPA and point out some common misunderstandings, then apply HF + RPA to the no-core shell model. Here the main issue is appropriate treatment of contamination by spurious center-of-mass motion.

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17

Hamber, Herbert W., and Lu Heng Sunny Yu. "Dyson’s Equations for Quantum Gravity in the Hartree–Fock Approximation." Symmetry 13, no. 1 (January 12, 2021): 120. http://dx.doi.org/10.3390/sym13010120.

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Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge–Wheeler lattice path integral lends itself well for that purpose. Nevertheless, lattice methods ultimately rely on extensive numerical calculations, leaving a desire for alternate methods that can be pursued analytically. In this work, we outline the Hartree–Fock approximation to quantum gravity, along lines which are analogous to what is done for scalar fields and gauge theories. The starting point is Dyson’s equations, a closed set of integral equations which relate various physical amplitudes involving graviton propagators, vertex functions, and proper self-energies. Such equations are in general difficult to solve, and as a result they are not very useful in practice, but nevertheless provide a basis for subsequent approximations. This is where the Hartree–Fock approximation comes in, whereby lowest order diagrams get partially dressed by the use of fully interacting Green’s function and self-energies, which then lead to a set of self-consistent integral equations. The resulting nonlinear equations for the graviton self-energy show some remarkable features that clearly distinguish it from the scalar and gauge theory cases. Specifically, for quantum gravity one finds a nontrivial ultraviolet fixed point in Newton’s constant G for spacetime dimensions greater than two, and nontrivial scaling dimensions between d=2 and d=4, above which one obtains Gaussian exponents. In addition, the Hartree–Fock approximation gives an explicit analytic expression for the renormalization group running of Newton’s constant, suggesting gravitational antiscreening with Newton’s constant slowly increasing on cosmological scales.

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18

Boldo, J. L., R. F. Turchiello, and R. Mota. "The two-band model and the metal-nonmetal transition in magnetlc systems." Ciência e Natura 15, no. 15 (December 13, 1993): 07. http://dx.doi.org/10.5902/2179460x26354.

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Using the two band model introduced by Mota and Coutinho-Filho, the metal-nonmetal transition is investigated by taking an approximate model Hamiltonian which takes into accout the hybridization of the bands, not included in the original model. A Green's function technique is used to obtain the hybrid bands inthe Hartree-Fock approximation. Investigating the phenomenon of metal-nonmetal transition, in general, increasing the intra-atomic interaction the tendency of the systems toward nonmetalic behavior increases. But, differently of previous results, for strong hybridization and small intra-atomic interaction, where the Hartree-fock approximation is valid, the opposite is observed. this may help to understand the difficult os observing pressure-induced nonmetal-metal transitions in magnetic systems.

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19

Benedikter, Niels. "Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 081101. http://dx.doi.org/10.1063/5.0091694.

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I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished: the semiclassical theory given by the Vlasov equation, the mean-field theory given by the Hartree–Fock equation, and the description of the dominant effects of non-trivial entanglement by the random phase approximation. Particular attention is given to the discussion of admissible initial data, and I present an example of a realistic quantum quench that can be approximated by Hartree–Fock dynamics.

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20

Co’, Giampaolo, and Stefano De Leo. "Hartree–Fock and random phase approximation theories in a many-fermion solvable model." Modern Physics Letters A 30, no. 36 (November 3, 2015): 1550196. http://dx.doi.org/10.1142/s0217732315501965.

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We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.

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21

BOKANOWSKI, OLIVIER, and NORBERT J. MAUSER. "LOCAL APPROXIMATION FOR THE HARTREE–FOCK EXCHANGE POTENTIAL: A DEFORMATION APPROACH." Mathematical Models and Methods in Applied Sciences 09, no. 06 (August 1999): 941–61. http://dx.doi.org/10.1142/s0218202599000439.

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We present a method for deriving local approximations of the exchange-term in the Hartree–Fock equation for a system of fermions interacting with a Coulomb-force. Within our model, we give a justification of the Slater-approximation where the exchange-term is replaced by the third root of the local density. Our approach is based on deformations, i.e. local scaling transformations of a constant density, combined with the "high density limit" of infinite number of particles.

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22

Suponitsky, Kyrill Yu, Vladimir G. Tsirelson, and Dirk Feil. "Electron-density-based calculations of intermolecular energy: case of urea." Acta Crystallographica Section A Foundations of Crystallography 55, no. 5 (September 1, 1999): 821–27. http://dx.doi.org/10.1107/s0108767399001993.

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The intermolecular interaction energy in crystalline urea has been calculated both from diffraction data and from the Hartree–Fock crystalline electron-density distribution, using a modified atom–atom approximation scheme. The electrostatic part of this energy has been calculated from the atomic multipole moments, obtained by adjustment of the multipole model to experimental X-ray and to theoretical Hartree–Fock structure amplitudes. To obtain the induction energy, multipole moments were calculated from structure amplitudes for the crystalline electron density and from those that refer to the electron density of a superposition of isolated molecules. This worked well for the calculation of the interaction energy from Hartree–Fock data (6% difference from the sublimation-energy value), but not for the interaction energy from experimental data, where the moments of the superposition have to come from Hartree–Fock calculations: the two sets of multipole moments are far too different. The uncertainty of the phases of the structure amplitudes, combined with systematic errors in the theoretical data and noise in the experimental values, may account for the discrepancies. The nature of the different contributions to intermolecular interactions for urea is examined.

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23

HU, J., H. TOKI, W. WEN, and H. SHEN. "RELATIVISTIC HARTREE-FOCK MODEL WITH SHORT RANGE CORRELATION IN NUCLEAR MATTER." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 2008–9. http://dx.doi.org/10.1142/s0217732310000885.

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We introduce the form factor and short range correlation in the relativistic Hartree-Fock approximation (RHFU) to study the properties of nuclear matter. We treat the short range correlation with the unitary correlation operator method (UCOM). In this framework, we can perfectly reproduce the equation of state of pure neutron matter obtained by the relativistic Brueckner-Hartree-Fock theory with the Bonn potential. We apply the RHFU model to symmetric nuclear matter. The contribution of ρ meson is cut down largely by the form factor of the size in the realistic nucleon-nucleon interaction. The short range correlation has a significant effect on the Fock energies of pion and ρ meson exchange interaction.

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24

Chong, Jacky J., and Zehua Zhao. "Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons." Annales Henri Poincaré 23, no. 2 (October 20, 2021): 615–73. http://dx.doi.org/10.1007/s00023-021-01100-w.

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25

Yatsyshin, P. I., R. G. Polozkov, V. K. Ivanov, and A. V. Solov'yov. "Structure of electron–positron clusters: Hartree–Fock approximation." Physica Scripta 80, no. 4 (October 2009): 048126. http://dx.doi.org/10.1088/0031-8949/80/04/048126.

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26

Quick, R. M., H. G. Miller, and B. J. Cole. "Reliability of the finite temperature Hartree-Fock approximation." Physical Review C 40, no. 2 (August 1, 1989): 993–97. http://dx.doi.org/10.1103/physrevc.40.993.

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27

Guimarães, F. B., B. V. Carlson, and T. Frederico. "Hartree-Fock-Bogoliubov approximation to relativistic nuclear matter." Physical Review C 54, no. 5 (November 1, 1996): 2385–98. http://dx.doi.org/10.1103/physrevc.54.2385.

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28

Su, Y. S., T. A. Kaplan, S. D. Mahanti, and J. F. Harrison. "Electronic structure ofLaMnO3in theab initiocrystal Hartree-Fock approximation." Physical Review B 61, no. 2 (January 1, 2000): 1324–29. http://dx.doi.org/10.1103/physrevb.61.1324.

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29

Lemm, J. C., and J. Uhlig. "Hartree-Fock Approximation for Inverse Many-Body Problems." Physical Review Letters 84, no. 20 (May 15, 2000): 4517–20. http://dx.doi.org/10.1103/physrevlett.84.4517.

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30

Marcos, S., M. López-Quelle, R. Niembro, and L. N. Savushkin. "Nuclear relativistic hartree-fock approximation with effective pions." Physics of Atomic Nuclei 75, no. 12 (December 2012): 1486–99. http://dx.doi.org/10.1134/s1063778812110166.

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31

Hong, Suklyun, and G. D. Mahan. "Spin-polarized Hartree-Fock approximation at nonzero temperatures." Physical Review B 51, no. 24 (June 15, 1995): 17417–30. http://dx.doi.org/10.1103/physrevb.51.17417.

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32

Bylander, D. M., and Leonard Kleinman. "Hartree-Fock core local-density-approximation valence pseudopotentials." Physical Review B 43, no. 14 (May 15, 1991): 12070–73. http://dx.doi.org/10.1103/physrevb.43.12070.

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33

Epperlein, Frank, Michael Schreiber, and Thomas Vojta. "Quantum Coulomb glass within a Hartree-Fock approximation." Physical Review B 56, no. 10 (September 1, 1997): 5890–96. http://dx.doi.org/10.1103/physrevb.56.5890.

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34

Schulze, H. J., A. Lejeune, J. Cugnon, M. Baldo, and U. Lombardo. "Hypernuclear matter in the Brueckner-Hartree-Fock approximation." Physics Letters B 355, no. 1-2 (July 1995): 21–26. http://dx.doi.org/10.1016/0370-2693(95)00665-8.

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35

Wu, S. S., and Y. J. Yao. "Renormalization of relativistic self-consistent Hartree-Fock approximation." European Physical Journal A 3, no. 1 (September 1998): 49–63. http://dx.doi.org/10.1007/s100500050147.

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36

Castorina, P., M. Consoli, and D. Zappalà. "Finite-temperature Hartree-Fock approximation to λΦ4 theory." Physics Letters B 201, no. 1 (January 1988): 90–94. http://dx.doi.org/10.1016/0370-2693(88)90086-x.

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37

Yanai, Takeshi, George I. Fann, Gregory Beylkin, and Robert J. Harrison. "Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response." Physical Chemistry Chemical Physics 17, no. 47 (2015): 31405–16. http://dx.doi.org/10.1039/c4cp05821f.

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A fully numerical method for the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation is presented in a multiresolution analysis (MRA) approach.

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38

Koch, Othmar. "Convergence of exponential Lawson-multistep methods for the MCTDHF equations." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 6 (November 2019): 2109–19. http://dx.doi.org/10.1051/m2an/2019033.

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We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree–Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.

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39

Kagawa, Takashi, and Gulzari Malli. "Relativistic Hartree–Fock–Roothaan wavefunctions for atoms." Canadian Journal of Chemistry 63, no. 7 (July 1, 1985): 1550–52. http://dx.doi.org/10.1139/v85-263.

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Relativistic Hartree–Fock–Roothaan (RHFR) wavefunctions have been calculated for a large number of atoms up to radon (Z = 86) under the point nucleus approximation using STO's as basis functions. The calculated total as well as orbital energies are in very good agreement with the corresponding results obtained by the numerical integration method.

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40

BARAN, A., J. A. SHEIKH, and W. NAZAREWICZ. "ADIABATIC MASS PARAMETERS FOR SPONTANEUS FISSION." International Journal of Modern Physics E 18, no. 04 (April 2009): 1054–57. http://dx.doi.org/10.1142/s0218301309013233.

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The collective mass tensor derived from the adiabatic time-dependent Hartree-Fock-Bogoliubov theory, perturbative cranking approximation, and the Gaussian overlap approximation to the generator coordinate method is discussed. Illustrative calculations are carried out for 252 Fm using the nuclear density functional theory with Skyrme interaction SkM* and seniority pairing.

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41

Nakajima, Takahito, Kimihiko Hirao, and Bun Chan. "Higher-order transition state approximation." Journal of Chemical Physics 156, no. 11 (March 21, 2022): 114112. http://dx.doi.org/10.1063/5.0086173.

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We generalize Slater’s transition state concept by deriving systematic higher-order transition state approximations. Numerical validation is performed by the calculation of transition energies for various excitations, including core, valence, and charge-transfer excitations, at Hartree–Fock and Kohn–Sham density functional theory levels. All higher-order transition state approximations introduced in this study accurately reproduce the results from delta self-consistent-field calculations. In particular, we demonstrate that the third-order generalized transition state (GTS3) approximation is a promising alternative to the original, owing to a good balance between the accuracy and computational cost. We also demonstrate that accurate and reliable results can be obtained with a low computational cost by combining the GTS3 approximation with the transition potential scheme.

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42

Kim, Jaewook, Kwangwoo Hong, Sunghwan Choi, Sang-Yeon Hwang, and Woo Youn Kim. "Configuration interaction singles based on the real-space numerical grid method: Kohn–Sham versus Hartree–Fock orbitals." Physical Chemistry Chemical Physics 17, no. 47 (2015): 31434–43. http://dx.doi.org/10.1039/c5cp00352k.

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We developed a program code of CIS based on a numerical grid method and showed that Kohn–Sham orbitals from the Krieger–Li–Iafrate (KLI) approximation provide better reference configurations for CIS than the standard Hartree–Fock and Kohn–Sham orbitals.

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43

Co’, Giampaolo. "Introducing the Random Phase Approximation Theory." Universe 9, no. 3 (March 7, 2023): 141. http://dx.doi.org/10.3390/universe9030141.

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Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of motion method, the Green function perturbation theory and the time-dependent Hartree–Fock theory. Each approach emphasizes specific aspects of the theory overlooked by the other methods. Extensions of the RPA secular equations to treat the continuum part of the excitation spectrum and also the pairing between the particles composing the system are presented. Theoretical approaches which overcome the intrinsic approximations of RPA are outlined.

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44

Khoromskaia, Venera, Boris Khoromskij, and Reinhold Schneider. "QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations." Computational Methods in Applied Mathematics 11, no. 3 (2011): 327–41. http://dx.doi.org/10.2478/cmam-2011-0018.

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AbstractIn this paper, the tensor-structured numerical evaluation of the Coulomb and exchange operators in the Hartree-Fock equation is supplemented by the usage of recent quantized-TT (QTT) formats. It leads to O(log n) complexity at computationally extensive stages in the rank-structured calculation with the respective 3D Hartree and exchange potentials discretized on large n×n×n Cartesian grids. The numerical examples for some volumetric organic molecules confirm that the QTT ranks of these potentials are nearly independent of the one-dimension grid size n. Thus, paradoxically, the complexity of the grid-based evaluation of the Coulumb and exchange matrices becomes almost independent of the grid size, being regulated only by the structure of a molecular system. As a result, the grid approximation of the Hartree-Fock equation allows to gain the high resolution with a guaranteed accuracy.

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Lauber, Stephanie M., Hayden C. Frye, and Calvin W. Johnson. "Benchmarking angular-momentum projected Hartree–Fock as an approximation." Journal of Physics G: Nuclear and Particle Physics 48, no. 9 (August 19, 2021): 095107. http://dx.doi.org/10.1088/1361-6471/ac1390.

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Loeser, J. G., and D. R. Herschbach. "Hartree–Fock approximation for D‐dimensional two‐electron atoms." Journal of Chemical Physics 84, no. 7 (April 1986): 3893–900. http://dx.doi.org/10.1063/1.450100.

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Ramschutz, J., and M. K. Weigel. "The optical potential in the relativistic Hartree-Fock approximation." Journal of Physics G: Nuclear and Particle Physics 20, no. 10 (October 1, 1994): 1633–48. http://dx.doi.org/10.1088/0954-3899/20/10/009.

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Hott, R. "GW-approximation energies and Hartree-Fock bands of semiconductors." Physical Review B 44, no. 3 (July 15, 1991): 1057–65. http://dx.doi.org/10.1103/physrevb.44.1057.

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Kumari, Kamlesh, and Deepak Kumar. "Thermodynamics of spin glasses in the Hartree-Fock approximation." Physical Review B 39, no. 16 (June 1, 1989): 12215–23. http://dx.doi.org/10.1103/physrevb.39.12215.

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Samsoen, D., P. Quentin, and J. Bartel. "Generalized routhian calculations within the Skyrme-Hartree-Fock approximation." Nuclear Physics A 652, no. 1 (May 1999): 34–60. http://dx.doi.org/10.1016/s0375-9474(99)00134-7.

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